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The homology of simplicial complement and the cohomology of the moment-angle complexes
A simplicial complement P is a sequence of subsets of [m] and the simplicial
complement P corresponds to a unique simplicial complex K with vertices in [m].
In this paper, we defined the homology of a simplicial complement
over a principle ideal domain k and proved
that is isomorphic to the Tor of the corresponding
face ring k(K) by the Taylor resolutions. As applications, we give methods to
compute the ring structure of Tor_{*,*}^{k[x]}(k(K), k)link_{K}\sigmastar_{K}\sigma$ and the cohomology of the generalized moment-angle complexes.Comment: 2 figure
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